Which of the two gases, air or carbon dioxide, has the lower final temperature as it is expanded isentropically from 800 kPa and 400°C to 100 kPa in a piston-cylinder device. Use room temperature specific heats.

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Netta00 Netta00 · Answer 1 · 2019-08-14T23:20:19+02:00

Answer:

Carbon dioxide have higher temperature at the final stage.

Explanation:

Given that

[tex]P_1=800 KPa,T_1=400 C,P_2=100 KPa[/tex]

We know that

γ=1.28 for carbon dioxide

γ=1.4 for air

For isentropic expansion

[tex]\dfrac{T_2}{T_1}=\left(\dfrac{P_2}{P_1}\right)^{\dfrac{\gamma -1}{\gamma}}[/tex]

Now for carbon dioxide γ=1.28

[tex]\dfrac{T_2}{673}=\left(\dfrac{100}{800}\right)^{\dfrac{1.28 -1}{1.28}}[/tex]

[tex]T_2=427.03 K[/tex]

Now for air γ=1.4

[tex]\dfrac{T_2}{673}=\left(\dfrac{100}{800}\right)^{\dfrac{1.4 -1}{1.4}}[/tex]

[tex]T_2=372.07 K[/tex]

So carbon dioxide have higher temperature at the final stage.